Laptop for the classroom

This isn't a music laptop question, but one for teaching kids in the classroom.
 
With the new detachable touch screen laptops, I recently had the idea of having a laptop connected to a projector, then detatching the screen and being able to face the kids whilst writing onto the screen, and having what I write of draw appear on the projected screen behind me.
 
So far the laptops I have seen have had the HDMI ports on the screen not the base, which kills the idea. Does anyone know of any with a laptop with a detachablle touchsceen with the HDMI on the base.
 
Or is there an alternative approach. Is there a programme that allows a normal tablet PC to feed a computer connected to a projecor.

Because I teach little-uns, it more for images and drawing than typing. I do have a spare laptop that's been superceeded by the one in my signature. So maybe a Tablet routed into this would be a better solution, with the HDMI and Audio connected to that as a base. Won't also be the death of the system should a kid step on the screen.
 
I'm guessing that with the detachable screens, they are basically a tablet with a keyboard and the base is generally little more than that. They weren't expensive, but I guess what I was hoping for the was for the bace still to be the PC and the screen to be more a remote screen. 

Apple's not cheap here, stings more that in the uk, gets taxed extra. I also don't ever want to go further into Apple land than my iPod shuffle.
 
The detachable screened laptops start at 250 quid here (8 Million), but as I've found I'd need a cable attached to the wrong part.
 
My budget won't be great, so the extra expense of wifi projector over a normal, and some sort of wifi audio device too, probably pushes it a bit far. Having looked at the windows surface, it seems pretty much the same as the laptops I was looking at from Asus and Acer.
 
Having the my old samsung laptop wired into the projector and speakers, with an extra tablet seems a sensible way forward. from the little research I've done, seems the wireless projectors can be a big drain of tablets, but I guess that's the same drain as wireless talking to the laptop.
 
I'm kind of planning ahead, simply because the company I work full seem full of ****, and I need to have a long term plan in place in my head. Maybe another option will come available in the meantime.